The Chaotic Properties of the Q-state Potts Model on the Bethe Lattice:Q<2

Details The Chaotic Properties of the Q-state Potts Model on the Bethe Lattice:Q<2 The Chaotic Properties of the Q-state Potts Model on the Bethe Lattice:Q<2

1998-06-11

arxiv.org/abs/cond-mat/9806146v1

Physics

Condensed Matter

13 pages, 5 figures

Scientific paper

The Q- state Potts model on the Bethe lattice is investigated for Q<2. The magnetization of this model exhibits a complicated behavior including both the period doubling bifurcation and chaos. The Lyapunov exponents of the Potts-Bethe map are considered as order parameters. We find a scaling behavior in the distribution of Lyapunov exponents in fully developed chaotic case. Using the thermodynamic formalism of dynamical systems have we investigated the nonanalytic behavior in the distribution of Lyapunov exponents and located the point of phase transition of the ''chaotic free energy''.

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